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if f(x)=1/2 x-6 what is the equation for f–1(x)?

A. f–1(x) = 2x + 6

B. f–1(x) = 2x – 6

C. f–1(x) = 2(x + 6)

D. f–1(x) = 2(x – 6)

Respuesta :

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Answer:

Option C [tex]f^{-1}(x)=2(x+6)[/tex]

Step-by-step explanation:

we have that

[tex]f(x)=\frac{1}{2}x-6[/tex]

Let

[tex]y=f(x)[/tex]

[tex]y=\frac{1}{2}x-6[/tex]

Exchange the variables x for y and y for x

[tex]x=\frac{1}{2}y-6[/tex]

Isolate the variable y

[tex]x+6=\frac{1}{2}y[/tex]

[tex]y=2(x+6)[/tex]

Let

[tex]f^{-1}(x)=y[/tex]

[tex]f^{-1}(x)=2(x+6)[/tex]

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